Quantum automorphism groups of finite quantum groups are classical

In a recent paper of Bhowmick, Skalski and Sołtan the notion of a quantum group of automorphisms of a finite quantum group was introduced and, for a given finite quantum group GG, existence of the universal quantum group acting on GG by automorphisms was proved. We show that this universal quantum group is in fact a classical group. The key ingredient of the proof is the use of multiplicative unitary operators, and we include a thorough discussion of this notion in the context of finite quantum groups.